The experience I have is from my buyers here in South Florida obtaining new policies. Besides the year the house was built, there are other factors that will impact the price. For instance, if the house has features that minimize damage in case of a hurricane. Also, the size of the property, if it has a pool and other structures, the proximity to the coast, the building materials, etc. I recommend that my buyers obtain a Wind Mitigation Inspection prior to getting the policy so that they can get certain discounts. The insurance companies here won't give the homeowner's the discounts unless the features are documented by a licensed inspector.
Usually the first year of the policy can be collected at closing. The policy price won't be added to your mortgage itself but the bank that you have your mortgage with will likely have an escrow account for you and will collect a portion from you every month in addition to your principal and interest in order to pay for the taxes and insurance when they are due, so you make one payment only.
Call different agencies and compare not only the price but the coverages too and see if they include replacement. Some homeowners have their deductibles higher so they pay less premium too.
I hope my answers were useful. Good luck on your search!
Coral Springs/Parkland Office